16
QuizMultiple Choice

Rational Functions — Test

Question 16 • Precalculus

The cost of catering a dinner is 11 point 9 5 dollars per person plus 25 dollars for delivery and setup. Which statement is true about the graph of the function that represents the average cost per person?

Answer
A
The vertical asymptote x is equal to 0 represents that the cost per person approaches 0 dollars as the number of people increases.
B
The horizontal asymptote y is equal to 11 point 9 5 represents that the cost per person approaches 11 point 9 5 dollars as the number of people increases.
C
The vertical asymptote x is equal to 11 point 9 5 represents that the cost per person approaches 11 point 9 5 dollars as the number of people increases.
D
The horizontal asymptote y is equal to 0 represents that the cost per person approaches 0 dollars as the number of people increases.

Explanation

For n people, the total cost is 11.95n + 25 dollars, so the average cost per person is (11.95n + 25)/n = 11.95 + 25/n. As the number of people increases, 25/n approaches 0, so the average cost approaches $11.95. Therefore, the graph has a horizontal asymptote y = 11.95, as stated in choice D.

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